Introduction
Overview of StatPower Pro
StatPower Pro is an advanced interactive tool designed to enhance
your understanding of statistical power, sample size calculation, and
research design. As students in CLTR6501, this app will serve as a
valuable resource in your journey to mastering the intricacies of
biostatistics and its application in clinical research.
Importance of Statistical Power and Sample Size in Research
In the realm of clinical research, the concepts of statistical power
and sample size are paramount. They form the foundation of robust study
designs and influence the validity and reliability of research findings.
Understanding these concepts is crucial for several reasons:
Ethical Considerations: Proper sample size
calculations ensure that studies are neither underpowered (risking false
negatives) nor overpowered (unnecessarily exposing more participants to
potential risks).
Resource Optimization: Accurate power analysis
helps allocate resources efficiently, preventing waste in overly large
studies or inadequate investment in underpowered studies.
Reproducibility: Studies with appropriate power
are more likely to produce reliable, reproducible results, contributing
to the overall integrity of scientific research.
Publication Bias: Understanding power can help
researchers and readers critically evaluate published studies,
particularly in the context of negative findings.
Key Features of StatPower Pro
StatPower Pro encompasses seven key features, each addressing crucial
aspects of statistical analysis and research design:
- Sample Size Calculator
- Test Type Comparison
- Type I & II Error Simulator
- CI Width Explorer
- One-sided vs Two-sided Tests Comparison
- ANOVA Calculator
- Chi-square Calculator
This guide will provide an in-depth exploration of each feature,
including theoretical background, practical applications, and tips for
interpretation.
StatPower Pro is freely accessible online. You can access the app
directly at: https://analytica.shinyapps.io/StatPower-Pro/
We encourage you to open this link and follow along with the examples
in this guide.
1. Sample Size Calculator
Theoretical Background
Understanding Statistical Power
Statistical power is a fundamental concept in hypothesis testing. It
represents the probability of correctly rejecting a false null
hypothesis, or in simpler terms, the likelihood of detecting a true
effect when it exists.
Mathematically, power is defined as:
Power = 1 - β
Where β is the probability of a Type II error (failing to reject a
false null hypothesis).
Factors Influencing Statistical Power
Several interconnected factors influence statistical power:
Effect Size: The magnitude of the difference or
relationship you’re trying to detect. It’s a measure of how substantial
the effect is in the population. Effect sizes are often categorized
as:
- Small: Subtle effects that might be challenging to detect
- Medium: Moderate effects that are typically visible to the naked
eye
- Large: Substantial effects that are obvious even in small
samples
Significance Level (α): The threshold for
declaring statistical significance, typically set at 0.05. It represents
the probability of a Type I error (rejecting a true null
hypothesis).
Sample Size: The number of participants or
observations in your study. Larger samples generally provide more power
but come with increased costs and logistical challenges.
Variability in the Data: The spread or
dispersion of the data. More variable data requires larger samples to
achieve the same power.
The Power-Sample Size Relationship
The relationship between power and sample size is not linear. As
sample size increases, power also increases, but with diminishing
returns. This relationship is crucial for understanding the trade-offs
in study design.
App Demo and Interpretation

The power curve visualizes the complex relationship between sample
size and statistical power:
- Blue Line: Represents how power increases with
sample size. Note the steep increase initially, followed by a flattening
of the curve.
- Red Dashed Horizontal Line: Indicates the
conventionally desired power level of 0.8 (80% power).
- Red Dashed Vertical Line: Shows the required sample
size to achieve 80% power.
In this example, we need approximately 64 subjects per group to
achieve 0.8 power. This point on the curve is critical:
- Below this point: Small increases in sample size
yield substantial gains in power.
- Above this point: We enter the realm of diminishing
returns, where large increases in sample size are needed for small gains
in power.
Practical Applications and Tips
Determining Minimum Sample Size: Use the app to
find the minimum sample size needed to achieve desired power (typically
0.8 or higher) for your specific effect size and significance
level.
Exploring Trade-offs: Adjust the effect size,
significance level, and desired power to understand how these changes
impact required sample size.
Feasibility Assessment: If the calculated sample
size is unfeasible, consider:
- Using more reliable measures to reduce variability
- Focusing on larger effect sizes (if justifiable)
- Employing within-subjects designs when possible
- Adjusting the desired power or significance level (with
caution)
Pilot Studies: Use the app to determine
appropriate sample sizes for pilot studies, which can help estimate
effect sizes for larger studies.
Interpreting Published Research: Apply the app
to evaluate the power of published studies, especially when interpreting
null results.
Case Study: Designing a Clinical Trial
Suppose you’re planning a clinical trial to test a new hypertension
medication. Based on previous studies, you expect a medium effect size
(d = 0.5) in blood pressure reduction compared to a placebo.
Using StatPower Pro: - Set effect size to 0.5 - Set desired power to
0.8 - Set significance level to 0.05 - Choose ‘Two-sample’ for the test
type
Result: You need approximately 64 participants per group (128
total).
Discussion Points: - Is this sample size feasible
for your study? - How would changing the effect size to 0.4 (smaller
effect) impact the required sample size? - What if you increased the
desired power to 0.9?
Exploring these scenarios in StatPower Pro can lead to informed
decisions about study design and resource allocation.
2. Test Type Comparison
Theoretical Background
Types of t-tests
T-tests are fundamental statistical tools used to compare means.
There are three main types of t-tests, each suited to different research
scenarios:
- Two-sample t-test:
- Purpose: Compares means of two independent groups
- Example: Comparing treatment effect between a control group and an
experimental group
- Null Hypothesis: μ1 = μ2 (The means of the two groups are
equal)
- One-sample t-test:
- Purpose: Compares one group mean to a known value
- Example: Comparing average patient recovery time to a standard
recovery time
- Null Hypothesis: μ = μ0 (The sample mean is equal to a specified
value)
- Paired t-test:
- Purpose: Compares two related means (often before and after
measurements)
- Example: Comparing pre-treatment and post-treatment scores for the
same group of patients
- Null Hypothesis: μd = 0 (The mean difference between paired
observations is zero)
How Test Choice Affects Sample Size
The choice of test affects the required sample size due to
differences in how these tests handle variability:
- Two-sample tests generally require the largest
sample sizes because they involve two separate groups, each with its own
variability.
- One-sample tests often need smaller samples as they
compare to a fixed value, reducing one source of variability.
- Paired tests typically require the smallest samples
because they control for individual differences, reducing within-group
variability.
App Demo and Interpretation

The bar chart compares required sample sizes for different t-test
types:
- Two-sample test: Requires the largest sample
size
- One-sample test: Requires a smaller sample size
compared to the two-sample test
- Paired test: Requires the smallest sample size
This visualization clearly demonstrates how the choice of test design
can significantly impact the required sample size, even when all other
parameters (effect size, power, significance level) remain constant.
Practical Applications and Tips
- Choosing the Appropriate Test:
- Base your choice on your research question and data structure, not
on minimizing sample size.
- Consider the nature of your groups (independent vs. related) and
your comparison target (another group vs. a known value).
- Leveraging Paired Designs:
- When feasible, paired designs can be more powerful and require
smaller samples.
- Useful in before-after studies or when natural pairing exists (e.g.,
twins, matched pairs).
- Reducing Variability in Two-sample Tests:
- Consider strategies to reduce between-group variability, such as
matching or stratification.
- Use of covariates in analysis (ANCOVA) can also help reduce
unexplained variability.
- Balancing Power and Practicality:
- While paired tests often require smaller samples, they may not
always be feasible or appropriate.
- Consider logistics, potential for dropout, and the nature of your
research question.
- Interpreting Published Research:
- When reviewing studies, consider how the choice of test might have
influenced the sample size and, consequently, the study’s power.
Case Study: Evaluating Treatment Efficacy
Scenario: You’re researching the efficacy of a new pain medication.
You have three potential study designs:
- Compare pain scores of treated patients to a known average
(One-sample)
- Compare pain scores between a treatment group and a control group
(Two-sample)
- Compare pain scores before and after treatment in the same patients
(Paired)
Using StatPower Pro, set: - Effect size: 0.5 (medium effect) -
Desired power: 0.8 - Significance level: 0.05
Results: - One-sample test: 34 participants - Two-sample test: 64
participants per group (128 total) - Paired test: 34 pairs (34
total)
Discussion Points: - How does each design affect
your total sample size? - What are the pros and cons of each approach
beyond sample size considerations? - How might practical constraints
(e.g., recruitment challenges, budget) influence your choice?
This example illustrates how StatPower Pro can inform crucial
decisions in study design, balancing statistical considerations with
practical constraints.
3. Type I & II Error Simulator
Theoretical Background
Understanding Type I and Type II Errors
In hypothesis testing, two types of errors can occur:
- Type I Error (α):
- Definition: Rejecting the null hypothesis when it’s actually true
(false positive)
- Probability: Set by the significance level, typically 0.05
- Example: Concluding a treatment is effective when it actually
isn’t
- Type II Error (β):
- Definition: Failing to reject the null hypothesis when it’s actually
false (false negative)
- Probability: 1 - Power
- Example: Failing to detect the effectiveness of a truly beneficial
treatment
The Relationship Between Errors and Power
- Power = 1 - β: The probability of correctly
rejecting a false null hypothesis
- There’s an inherent trade-off: decreasing one type of error often
increases the other
Factors Influencing Error Rates
- Sample Size: Larger samples generally reduce both
types of errors
- Effect Size: Larger effects are easier to detect,
reducing Type II errors
- Significance Level: Stricter levels (smaller α)
reduce Type I errors but increase Type II errors
- Variability: Higher variability in data increases
both types of errors
App Demo and Interpretation

This visualization helps understand the interplay between Type I and
II errors:
- Blue Distribution: Represents the null hypothesis
(H0) - the distribution of test statistics if there’s no effect
- Green Distribution: Represents the alternative
hypothesis (H1) - the distribution if there is an effect
- Red Dashed Lines: Critical values that determine
the rejection region for H0
- Type I Error: Area under the blue curve beyond the
red lines
- Type II Error: Area under the green curve between
the red lines
Key Observations: - The overlap between the distributions represents
the potential for errors - Moving the red lines (changing α) affects
both error types - Separating the distributions (increasing effect size
or sample size) reduces both errors
Practical Applications and Tips
- Balancing Error Types:
- Consider the relative costs of each error type in your research
context
- In medical studies, false negatives (missing a real effect) might be
more concerning than false positives
- Sample Size Planning:
- Use the simulator to understand how increasing sample size affects
both error types
- Find the optimal sample size that balances error reduction with
practical constraints
- Setting Significance Levels:
- Explore how different α levels affect power and Type II error
rates
- Consider using different α levels for exploratory vs. confirmatory
research
- Effect Size Considerations:
- Use the simulator to see how different effect sizes impact error
rates
- This can help in planning studies for detecting smaller, more
realistic effects
- Understanding Power:
- Visualize how power (1 - β) changes with different parameters
- Use this understanding to justify power calculations in research
proposals
Case Study: Clinical Trial Decision Making
Scenario: You’re designing a clinical trial for a new cancer
treatment. The stakes are high: - A Type I error could lead to approving
an ineffective treatment (wasted resources, potential harm to patients)
- A Type II error could mean missing an effective treatment (lost
opportunity to save lives)
Using StatPower Pro: - Set effect size to 0.4 (a moderate effect for
cancer treatments) - Vary sample sizes and significance levels
Discussion Points: - How does changing the
significance level from 0.05 to 0.01 affect Type I and II errors? - What
sample size would you need to achieve both low Type I and Type II error
rates? - Given the high stakes, would you prioritize minimizing Type I
or Type II errors? Why?
This example demonstrates how the Type I & II Error Simulator can
inform critical decisions in high-stakes research, balancing statistical
rigor with ethical considerations and practical constraints.
4. CI Width Explorer
Theoretical Background
Understanding Confidence Intervals
Confidence Intervals (CI) provide a range of plausible values for a
population parameter:
- Definition: A CI is a range of values that you can be confident (to
a specified degree) contains the true population parameter
- Interpretation: A 95% CI means that if you repeated the study many
times, 95% of the CIs would contain the true population parameter
Factors Influencing CI Width
- Sample Size: Larger samples lead to narrower
CIs
- Variability in the Data: More variable data results
in wider CIs
- Confidence Level: Higher confidence levels (e.g.,
99% vs 95%) result in wider CIs
- Standard Error: CI width is directly related to the
standard error of the estimate
Importance of CI Width
- Precision: Narrower CIs indicate more precise estimates
- Practical Significance: CI width helps interpret the practical
importance of results
- Study Planning: Understanding CI width helps in determining
appropriate sample sizes for desired precision
App Demo and Interpretation

The curve shows how CI width decreases as sample size increases:
- Y-axis: Represents the width of the confidence interval
- X-axis: Represents the sample size
- Curve Shape: Demonstrates an inverse relationship between sample
size and CI width
Key Observations: - Rapid decrease in CI width for small sample sizes
- The rate of decrease slows for larger sample sizes (diminishing
returns) - This relationship helps researchers balance precision with
resource constraints
Practical Applications and Tips
- Determining Sample Size for Desired Precision:
- Use the app to find the sample size needed for a specific CI
width
- Consider the practical implications of different CI widths in your
field
- Balancing Precision and Resources:
- Identify the point of diminishing returns where increasing sample
size yields minimal improvements in precision
- Use this to justify sample size decisions in research proposals
- Interpreting Published Research:
- Use the app to understand the precision of estimates in published
studies
- Evaluate whether the CI width in a study is narrow enough for
meaningful conclusions
- Planning Pilot Studies:
- Determine appropriate sample sizes for pilot studies to estimate
parameters with reasonable precision
- Considering Practical Significance:
- Relate CI width to clinically or practically significant differences
in your field
- Ensure that your CI is narrow enough to make meaningful
inferences
Case Study: Estimating Population Parameters
Scenario: You’re conducting a study to estimate the average blood
pressure in a population of patients with hypertension.
Using StatPower Pro: - Set the confidence level to 95% - Assume a
standard deviation of 15 mmHg (based on previous studies) - Explore
different sample sizes
Results: - n = 50: CI width ≈ 8.3 mmHg - n = 100: CI width ≈ 5.9 mmHg
- n = 200: CI width ≈ 4.1 mmHg
Discussion Points: - How precise does your estimate
need to be for clinical relevance? - At what point do increases in
sample size yield diminishing returns in precision? - How would changing
the confidence level to 99% affect the CI width?
This example illustrates how the CI Width Explorer can guide
decisions about sample size and precision in estimation studies.
5. One-sided vs Two-sided Tests
Theoretical Background
Understanding One-sided and Two-sided Tests
- One-sided (Directional) Tests:
- Hypothesis about the direction of effect (greater than or less
than)
- Example H1: μ > μ0 or μ < μ0
- Used when there’s a clear expectation about the direction of the
effect
- Two-sided (Non-directional) Tests:
- Hypothesis about any difference (not equal to)
- Example H1: μ ≠ μ0
- Used when the direction of the effect is uncertain or not
specified
Power Implications
- One-sided tests generally have more power for a given sample
size
- This is because all the α is allocated to one tail of the
distribution in a one-sided test
Ethical and Practical Considerations
- One-sided tests can miss unexpected effects in the opposite
direction
- The choice between one-sided and two-sided should be based on
research questions and prior knowledge, not just to maximize power
App Demo and Interpretation

The comparison shows: - Required sample size for one-sided test -
Required sample size for two-sided test - The difference in sample size
between the two approaches
Key Observations: - One-sided tests require smaller sample sizes for
the same power - The difference in required sample size can be
substantial, especially for smaller effect sizes
Practical Applications and Tips
- Choosing Between One-sided and Two-sided Tests:
- Use one-sided tests only when you have a strong theoretical or
practical reason to expect an effect in a specific direction
- Consider the risks of missing unexpected effects when using
one-sided tests
- Justifying Test Choice:
- Use the app to quantify the sample size implications of your test
choice
- Be prepared to justify one-sided tests in your research protocol or
publication
- Sensitivity Analysis:
- Explore how the choice between one-sided and two-sided tests affects
your study’s feasibility
- Consider running analyses both ways if the choice significantly
impacts your ability to conduct the study
- Ethical Considerations:
- Discuss the ethical implications of choosing a one-sided test,
especially in clinical trials
- Consider whether a one-sided test might be viewed as “fishing for
significance”
- Reporting Results:
- If using a one-sided test, clearly state this in your methods and
results
- Consider reporting two-sided p-values alongside one-sided results
for transparency
Case Study: Testing a New Drug
Scenario: You’re testing a new drug expected to lower cholesterol
levels.
Using StatPower Pro: - Set effect size to 0.3 (a modest effect) - Set
desired power to 0.8 - Set significance level to 0.05
Results: - One-sided test: 138 participants - Two-sided test: 176
participants
Discussion Points: - Given prior research, is a
one-sided test justifiable? - How would you defend your choice of a
one-sided or two-sided test to an ethics committee? - If unexpected
results emerge (e.g., the drug increases cholesterol), how would your
choice of test affect your ability to detect this?
This example demonstrates how the choice between one-sided and
two-sided tests involves balancing statistical power, ethical
considerations, and scientific rigor.
6. ANOVA Calculator
Theoretical Background
Understanding ANOVA (Analysis of Variance)
- Purpose: Compares means across multiple groups (three or more)
- Null Hypothesis: All group means are equal (μ1 = μ2 = μ3 = … =
μk)
- Alternative Hypothesis: At least one group mean is different
Factors Affecting Power in ANOVA
- Number of Groups: Generally, more groups require
larger total sample sizes
- Effect Size: In ANOVA, often expressed as Cohen’s f
- f = 0.10 is considered a small effect
- f = 0.25 is a medium effect
- f = 0.40 is a large effect
- Significance Level: Typically set at 0.05
- Desired Power: Conventionally aimed at 0.8 or
higher
Importance in Research Design
- Crucial for studies comparing multiple treatments or conditions
- Helps determine the sample size needed to detect differences among
groups
- Informs decisions about the number of groups to include in a
study
App Demo and Interpretation

The plot shows: - X-axis: Number of groups in the ANOVA - Y-axis:
Statistical power achieved - Curve: Relationship between number of
groups and power, given fixed total sample size and effect size
Key Observations: - Power generally increases with more groups (given
fixed effect size and total sample size) - The rate of power increase
diminishes as the number of groups grows - This relationship helps
researchers balance the number of groups with achievable power
Practical Applications and Tips
- Determining Sample Size:
- Use the app to calculate the required sample size per group for a
desired power level
- Consider practical constraints when deciding on the number of
groups
- Exploring Trade-offs:
- Investigate how changing the number of groups affects required
sample size
- Balance the benefits of more groups (increased power) with the costs
(increased complexity, resources)
- Effect Size Considerations:
- Use the app to understand how different effect sizes impact power
and sample size requirements
- Consider running calculations for a range of plausible effect
sizes
- Planning Multi-arm Studies:
- Use the ANOVA calculator to design efficient multi-arm trials
- Explore how adding or removing study arms affects overall power and
feasibility
- Post-hoc Considerations:
- Remember that ANOVA only tells you if there are any differences
among groups
- Plan for post-hoc tests to determine which specific groups
differ
Case Study: Comparing Multiple Treatments
Scenario: You’re planning a study to compare the effectiveness of
four different exercise programs on weight loss.
Using StatPower Pro: - Set the number of groups to 4 - Assume a
medium effect size (f = 0.25) - Set desired power to 0.8 - Set
significance level to 0.05
Results: - Required sample size: 45 participants per group (180
total)
Discussion Points: - How would adding a fifth group
(e.g., a control group) affect your sample size requirements? - If you
can only recruit 120 participants total, how would this affect your
study’s power? - How might you adjust your design if the effect size is
smaller (f = 0.15)?
This example illustrates how the ANOVA Calculator can guide decisions
in complex study designs, helping researchers balance statistical power
with practical constraints.
7. Chi-square Calculator
Theoretical Background
Understanding Chi-square Tests
- Purpose: Analyze categorical data and test relationships between
categorical variables
- Common uses:
- Test of Independence: Examines the relationship between two
categorical variables
- Goodness of Fit Test: Compares observed frequencies to expected
frequencies
Key Concepts in Chi-square Analysis
- Degrees of Freedom (df): Related to the number of
categories in your data
- For test of independence: df = (r-1)(c-1), where r = number of rows,
c = number of columns
- For goodness of fit: df = k-1, where k = number of categories
- Effect Size (w): Measures the magnitude of the
difference between observed and expected frequencies
- w = 0.1 is considered a small effect
- w = 0.3 is a medium effect
- w = 0.5 is a large effect
- Sample Size: Affects the power to detect
significant relationships or differences
Importance in Research
- Crucial for studies involving categorical outcomes
- Helps determine sample size needed to detect associations between
categorical variables
- Important in fields like epidemiology, social sciences, and clinical
research
App Demo and Interpretation

The plot shows: - X-axis: Effect size (w) - Y-axis: Required sample
size - Multiple lines: Represent different degrees of freedom
Key Observations: - Required sample size decreases as effect size
increases - More degrees of freedom (more categories) generally require
larger sample sizes - The relationship between effect size and sample
size is non-linear
Practical Applications and Tips
- Sample Size Determination:
- Use the app to calculate required sample size based on expected
effect size and degrees of freedom
- Consider running calculations for a range of plausible effect
sizes
- Study Design Decisions:
- Explore how different categorizations (affecting degrees of freedom)
impact sample size requirements
- Balance the desire for detailed categories with power
considerations
- Feasibility Assessment:
- Use the calculator to determine if your planned sample size is
sufficient for your expected effect size
- Adjust study design or expectations if required sample sizes are not
feasible
- Interpreting Published Research:
- Use the app to evaluate the power of published chi-square analyses,
especially for non-significant results
- Minimum Expected Frequencies:
- Remember that chi-square tests require minimum expected frequencies
in each cell (typically > 5)
- Use the app to ensure your sample size is large enough to meet this
assumption
Case Study: Analyzing Treatment Preferences
Scenario: You’re studying the relationship between age groups (young,
middle-aged, elderly) and preferences for three types of hypertension
treatments (medication, lifestyle changes, combination).
Using StatPower Pro: - Degrees of freedom: (3-1)(3-1) = 4 - Assume a
medium effect size (w = 0.3) - Set desired power to 0.8 - Set
significance level to 0.05
Results: - Required sample size: 133 participants
Discussion Points: - How would collapsing age groups
into two categories affect your sample size requirement? - If you can
only recruit 100 participants, what effect size would you be able to
detect? - How might you adjust your design if you expect a smaller
effect (w = 0.2)?
This example demonstrates how the Chi-square Calculator can inform
decisions in studies involving categorical data, helping researchers
design adequately powered studies for detecting associations between
categorical variables.
Conclusion
Integrating StatPower Pro in Research Design
StatPower Pro is a powerful tool that can significantly enhance your
approach to research design and statistical analysis. By providing
interactive visualizations and instant calculations, it allows you
to:
- Make informed decisions about sample size and study design
- Understand the trade-offs between different statistical
approaches
- Explore the implications of various parameter choices on your
study’s power and precision
Key Takeaways
- Power, Effect Size, and Sample Size are
Interconnected:
- Changing one parameter affects the others
- Use StatPower Pro to explore these relationships in your specific
research context
- Different Test Types Have Different Requirements:
- Choose the appropriate test based on your research question and data
structure
- Understand how test choice affects sample size and power
- Balance Statistical and Practical Significance:
- Consider both the statistical power of your study and the practical
importance of the effects you’re trying to detect
- Use confidence interval widths to interpret the precision and
practical significance of your results
- Ethical Considerations in Study Design:
- Use StatPower Pro to ensure your studies are neither underpowered
(risking false negatives) nor overpowered (unnecessarily exposing
participants to potential risks)
- Consider the ethical implications of your choices in test direction
and sample size
- Flexibility in Research Planning:
- Explore multiple scenarios and designs before finalizing your
research plan
- Use StatPower Pro to justify your methodological choices in research
proposals and publications
Future Directions
As you progress in your research career, continue to use tools like
StatPower Pro to:
- Stay updated on best practices in statistical power and sample size
determination
- Critically evaluate published research in terms of statistical power
and precision
- Design more efficient and ethical studies that optimize resource use
while maintaining scientific rigor
Remember, while StatPower Pro is a powerful aid in research design,
it should be used in conjunction with subject matter expertise, ethical
considerations, and practical constraints. The app is a tool to inform
your decisions, not to make them for you.
Accessing StatPower Pro
To start using StatPower Pro and apply the concepts discussed in this
guide, visit:
https://analytica.shinyapps.io/StatPower-Pro/
This web-based application is free to use and does not require any
installation. Simply click the link to begin exploring the powerful
features of StatPower Pro in your browser.
Remember to refer back to this guide as you use the app for detailed
explanations and interpretations of each feature.
Additional Resources
For further exploration of the concepts covered in this guide:
Cohen, J. (1988). Statistical Power Analysis for the Behavioral
Sciences. This classic text provides in-depth coverage of effect sizes
and power analysis.
Lakens, D. (2013). Calculating and reporting effect sizes to
facilitate cumulative science: a practical primer for t-tests and
ANOVAs. Frontiers in Psychology. An excellent modern resource on effect
sizes and their interpretation.
Button, K. S., et al. (2013). Power failure: why small sample
size undermines the reliability of neuroscience. Nature Reviews
Neuroscience. A critical examination of the consequences of underpowered
studies.
G*Power: Free software for power analysis (http://www.gpower.hhu.de/). Another useful tool for
power analysis, offering some features complementary to StatPower
Pro.
Harvard Online Statistics Course (https://online-learning.harvard.edu/course/statistics-and-r).
A comprehensive online course covering many of the statistical concepts
discussed in this guide.
For questions, feedback, or assistance with StatPower Pro, please
contact: Dr. Aous Abdo (aous.abdo@analyticadss.com)
Remember, mastering these concepts is a journey. StatPower Pro is
here to support you every step of the way in your pursuit of rigorous
and impactful research.